The University of Akron, Department of Mathematics, Akron, OH 44325-4002, USA.
Math Biosci. 2013 Jul;244(1):29-39. doi: 10.1016/j.mbs.2013.04.006. Epub 2013 Apr 27.
Biofilms are found within the lungs of patients with chronic pulmonary infections, in particular patients with cystic fibrosis, and are the major cause of morbidity and mortality for these patients. The work presented here is part of a large interdisciplinary effort to develop an effective drug delivery system and treatment strategy to kill biofilms growing in the lung. The treatment strategy exploits silver-based antimicrobials, in particular, silver carbene complexes (SCC). This manuscript presents a mathematical model describing the growth of a biofilm and predicts the response of a biofilm to several basic treatment strategies. The continuum model is composed of a set of reaction-diffusion equations for the transport of soluble components (nutrient and antimicrobial), coupled to a set of reaction-advection equations for the particulate components (living, inert, and persister bacteria, extracellular polymeric substance, and void). We explore the efficacy of delivering SCC both in an aqueous solution and in biodegradable polymer nanoparticles. Minimum bactericidal concentration (MBC) levels of antimicrobial in both free and nanoparticle-encapsulated forms are estimated. Antimicrobial treatment demonstrates a biphasic killing phenomenon, where the active bacterial population is killed quickly followed by a slower killing rate, which indicates the presence of a persister population. Finally, our results suggest that a biofilm with a ready supply of nutrient throughout its depth has fewer persister bacteria and hence may be easier to treat than one with less nutrient.
生物膜存在于慢性肺部感染患者的肺部,特别是囊性纤维化患者的肺部,是这些患者发病和死亡的主要原因。这里介绍的工作是一个大型跨学科努力的一部分,旨在开发有效的药物输送系统和治疗策略来杀死肺部生长的生物膜。该治疗策略利用基于银的抗菌剂,特别是银卡宾复合物(SCC)。本文提出了一个描述生物膜生长的数学模型,并预测了生物膜对几种基本治疗策略的反应。连续体模型由一组用于可溶性成分(营养物和抗菌剂)传输的反应扩散方程组成,与一组用于颗粒成分(活的、惰性的和持久细菌、细胞外聚合物物质和空隙)的反应-对流方程耦合。我们探索了在水溶液和可生物降解聚合物纳米颗粒中输送 SCC 的效果。以游离形式和纳米颗粒包封形式存在的抗菌剂的最低杀菌浓度(MBC)水平进行了估计。抗菌治疗表现出两相杀菌现象,其中活性细菌种群迅速被杀死,然后是较慢的杀死速率,这表明存在持久细菌种群。最后,我们的结果表明,在整个深度都有充足营养供应的生物膜中,持久细菌较少,因此可能比营养较少的生物膜更容易治疗。